The area of a circle is 1386 sq. cm, find its circumference.

Answer

To find the circumference of a circle when the area is given, we can follow these steps:

### Step 1: Write down the formula for the area of a circle.
The formula for the area \( A \) of a circle is given by:
\[ A = \pi r^2 \]
where \( r \) is the radius of the circle.

### Step 2: Substitute the given area into the formula.
We know that the area of the circle is \( 1386 \, \text{sq. cm} \). Therefore, we can set up the equation:
\[ \pi r^2 = 1386 \]

### Step 3: Use the value of \( \pi \).
For calculations, we can use \( \pi \approx \frac{22}{7} \). Substituting this into the equation gives:
\[ \frac{22}{7} r^2 = 1386 \]

### Step 4: Solve for \( r^2 \).
To eliminate the fraction, multiply both sides by \( 7 \):
\[ 22 r^2 = 1386 \times 7 \]
Calculating \( 1386 \times 7 \):
\[ 1386 \times 7 = 9702 \]
So, we have:
\[ 22 r^2 = 9702 \]

### Step 5: Divide by 22 to isolate \( r^2 \).
\[ r^2 = \frac{9702}{22} \]
Calculating \( \frac{9702}{22} \):
\[ r^2 = 441 \]

### Step 6: Take the square root to find \( r \).
\[ r = \sqrt{441} = 21 \, \text{cm} \]

### Step 7: Write down the formula for the circumference of a circle.
The formula for the circumference \( C \) of a circle is given by:
\[ C = 2\pi r \]

### Step 8: Substitute the value of \( r \) into the circumference formula.
Using \( \pi \approx \frac{22}{7} \) and \( r = 21 \, \text{cm} \):
\[ C = 2 \times \frac{22}{7} \times 21 \]

### Step 9: Simplify the expression.
\[ C = \frac{44}{7} \times 21 \]
Calculating \( \frac{44 \times 21}{7} \):
\[ C = \frac{924}{7} = 132 \, \text{cm} \]

### Final Answer:
The circumference of the circle is \( 132 \, \text{cm} \).

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